About

1.2.8 Example

A particle moves in a simple harmonic motion between O to A and B and back to O as shown. The positions B, B1, O, A1 and A are equally spaced. The time taken to travel from A to B is 5.00 s and the distance AB is 4.00 m.

a)    Write an equation to represent the given simple harmonic motion.
b)    During one cycle, find the time that the particle stays in the region:
i)     A-A1    
ii)     A1-B1     

[ x = 0.200 sin (0.628 t) , 0.833 s , 3.33 s ]

Hint:

1.2.8.1 Solution:

a) since x0 is half of AB = 4 m

x0 = 2.00 m

the equation is x = x0 sin(ωt)

to find ω, and we can given T, we use

$\omega =\genfrac{}{}{0.1ex}{}{2\pi }{T}=\genfrac{}{}{0.1ex}{}{2\pi }{\left(5\right)\left(2\right)}=0.628$

thus the equation is x = 2.00 sin(0.628t)

b) the strategy is to find the time which all the points B, B1, O, A1 and A occurs.

to find time from A to A1,

when x = A1 = 1.00, imply 1.00 = 2.00 sin (0.628t), therefore t_A1 = 0.833 s

similarly, when x = A = 2.00, imply 2.00 = 2.00sin (0.628t), therefore t_A = 2.50 s

time from A1 to A = t_A -t_A1 = 2.50 - 0.833 = 1.66 s

therefore time from A1 to A to A1 = (1.66)(2) = 3.33 s

b) since we know t 0 to A1 = 0.833 s

by comparing the 4 equal sections of OA1 = A1O = OB1 = B1O = 0.833 s

the total time spent inside A1B1 = (4)(0.833) = 3.33 s

1.2.8.2 Model

1. Run Sim
2. http://iwant2study.org/ospsg/index.php/77

 

Translations

Code	Language		Translator	Run

Software Requirements

	Android	iOS	Windows	MacOS
with best with	Chrome	Chrome	Chrome	Chrome
support full-screen?	Yes. Chrome/Opera No. Firefox/ Samsung Internet	Not yet	Yes	Yes
cannot work on	some mobile browser that don't understand JavaScript such as.....		cannot work on Internet Explorer 9 and below

 

Credits

This email address is being protected from spambots. You need JavaScript enabled to view it.

end faq